You can drop team's avq by keeping players white skills high and grey low, like this player, for example:
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At the first sight you'll think he's a BS player, but after you have a closer look his actual avq is about 150%:
Click image for larger version. 

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He's naturally developed, no tanking, no token training, he's a bit slow at the beginning of the season, but he'll come around:
Click image for larger version. 

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